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A Rapid Numerical Algorithm to Compute Matrix Inversion

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  • F. Soleymani

Abstract

The aim of the present work is to suggest and establish a numerical algorithm based on matrix multiplications for computing approximate inverses. It is shown theoretically that the scheme possesses seventh-order convergence, and thus it rapidly converges. Some discussions on the choice of the initial value to preserve the convergence rate are given, and it is also shown in numerical examples that the proposed scheme can easily be taken into account to provide robust preconditioners.

Suggested Citation

  • F. Soleymani, 2012. "A Rapid Numerical Algorithm to Compute Matrix Inversion," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-11, September.
    • Handle: RePEc:hin:jijmms:134653
    DOI: 10.1155/2012/134653
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    References listed on IDEAS

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    1. Davod Khojasteh Salkuyeh & Hadi Roohani, 2009. "On the Relation between the AINV and the FAPINV Algorithms," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2009, pages 1-6, November.
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    Cited by:

    1. Cordero, Alicia & Soto-Quiros, Pablo & Torregrosa, Juan R., 2021. "A general class of arbitrary order iterative methods for computing generalized inverses," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    2. Kansal, Munish & Kumar, Sanjeev & Kaur, Manpreet, 2022. "An efficient matrix iteration family for finding the generalized outer inverse," Applied Mathematics and Computation, Elsevier, vol. 430(C).

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